MEASUREMENT • OF HEAT... TRANSFER COEFFICIENT IN

CONCENTRIC AND ECCENTRIC ANNULI

by

WASIUDDIN CHOUDHURY

B.Sc.Eng. , University of Dacca, 1958

A THESIS SUBMITTED IN.PARTIAL FULFILMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

i n the Department

of

Mechanical Engineering

We accept this thesis as conforming to the

required standard

THE UNIVERSITY OF BRITISH COLUMBIA

APRIL, 1963

i i

In presenting this thesis i n p a r t i a l fulfilment of the

requirements for an advanced degree at the University of Br i t i sh

Columbia, I agree that the Library shal l make i t freely available

for reference and study. .1 further agree that permission for ex­

tensive copying of this thesis for scholarly purposes may be granted

by the Head of my Department or by his representatives. It is

understood that copying or publications of this thesis for f inancial

gain shal l not be allowed without my written permission.

Department of Mechanical Engineering,

The University of Br i t i sh Columbia,

Vancouver 8, Canada.

A p r i l , 1963.

i i i

ABSTRACT

Heat transfer coefficients were measured at the inner wall

of smooth concentric and eccentric annuli. The annuli were formed by

an,outer plast ic tube of 3 i n . inside diameter and an inner core

cylinder of 1 i n . outside diameter. A i r at room temperature was;

allowed to flow through the annuli at a Reynolds number range from

15,000 to 65,000.

The measurement of heat transfer coefficient was made by

a transient heat transfer test technique. The method consisted i n

establishing an i n i t i a l temperature gradient between the f l u i d and

a so l id body mounted on the core cylinder by heating, then observing

and recording the temperature-time history of the body as i t returned

to equilibrium condition with the f l u i d stream. The heat transfer

coefficient was calculated from this record.

The f i n a l results were presented i n graphical form.showing

variations of Nusselt number with Reynolds number. The results of the

concentric annulus tests agreed favourably with those predicted by

Wiegand (2) and Monrad and Pelton (3)' The effect of eccentricity

was to reduce the heat transfer coefficient although the general

trend was identical to that in the concentric annulus case.

It was observed that the decrease of heat transfer coef­

f ic ient was not l inear ly related to the eccentricity of the core

cylinder. The effect of eccentricity was more pronounced in the

range 0 < e < 0.5 where the value of heat transfer coefficient de­

creased considerably.

X

•ACKNOWLEDGEMENT

The author would l ike to thank the many persons whose

direct or indirect assistance has made this report possible. He

should l ike to mention some of them by name:

Professor W. 0. Richmond deserves many thanks for his

continued encouragement and assistance during a l l phases of the

work.

Professors V. J . Modi, N. Epstein) C . - A . Brockely and

Mr. J . D. Denton for many valuable discussions during different

phases of the project.

Professor W . A . Wolfe who suggested the present.topic and

through whose i n i t i a l efforts the project was started.

F ina l ly the author would l ike to express his thanks

for the permission to use the Computing Centre at the University

of Br i t i sh Columbia and the National Research Council of Canada

for providing funds to make this research possible.

i v

TABLE OF CONTENTS

Page

CHAPTER I

Introduction.. . . . . . . . . . . . . . . . 1

Definitions of Terms Used 2

Review of 'Literature on-Annuli ' 3

CHAPTER II

The Transient Test Technique 9

Discussion of Assumptions . . . . . . 12

CHAPTER III

Apparatus 15

instrumentation . . . . . . . . . . . . 2h

CHAPTER IV

Experimental Procedure 27

Presentation of Results . . . . . . . . . . . . . . . . . . . . 28

Discussion of Results 3-

CHAPTER V

Conclusions . . . . . . . . . . . . . . . Mi-

Recommendations k-5

BIBLIOGRAPHY k6

APPENDIX I

A i r Metering System . . . . . . . . ^9

V

Page

APPENDIX II

Physical Properties and Constants of the Thermal . Capacitors 52

APPENDIX III .

Physical Properties of Air 53

APPENDIX TV

Sample Calculations 56

APPENDIX V

Tables of Experimental Results 57

v i

LIST OF FIGURES

Page

1. . Schematic Layout.of the Concentric Annulus Tests . . . 19

2. Test Models and Mounting Structures . . . . . . . . . 20

3. Schematic Layout of the Eccentric Annulus Tests . . . 21

k. Method of Supporting Inner Tube . . . . . . . . . . . . . . . 22

5. Photographs of Test Section and Capacitors . 23

6. Thermocouple Circu i t . . . . . . . . . . . . . . . . . . . . 26

7« A Typical Temperature-Time Relation as Obtained on

the Recorder . . . . . . . . . . . . . . . . . . . . . . . . . . 29

.8. Heat Transfer at Inner Wall of Annulus, e = 0. . . . . : 30

9« Heat Transfer at Inner Wall of Annulus,.e.= Q'.25 .... .31

10. Heat Transfer at Inner Wall of Annulus, e = 0.50 , . . 32

11. Heat Transfer at Inner Wall of Annulus, e = 1.0 . . . .33

12. Variation of Nusselt Number with Reynolds Number and Eccentricity Parameter . 35

13. Variat ion of Heat Transfer Coefficient with Inner Tube Eccentricity . . . . . 36

l U . Comparison of Heat Transfer Data Obtained by Capacitors No. 1 and No. 2 . . ..................... 38

15« A Typical Semi-Log Plot of Dimensionless Temperature

with Time kl

16. Thermocouple Locations in the Capacitor k2

17. Dynamic Viscosity of A i r at Atmospheric Pressure . . . 5

18. Thermal Conductivity of Air at Atmospheric Pressure. . 55

v i i

LIST OF TABLES Page

; I i Details of Orifice 51

II. Properties of Thermal Capacitors 52

III. Biot Number of the Capacitors . . . . . . . . . . . . . . . . . 52

TV. Temperature-Time Data for Capacitor No. 1, e = 0 . . 58

V. Data for Computing Reynolds and Nusselt Numbers

for Capacitor No. 1, e = 0 ... 59

VI. Temperature-Time Data for Capacitor No. 1,. e = O.25. 60

VII. Data for Computing Reynolds and Nusselt Numbers for

Capacitor No. 1/ e .= 0.25 . . . . . . . . . . . . . 6 l VIII. Temperature-Time Data for Capacitor No..1, e = 0.50. 62

IX. Data for Computing Reynolds and Nusselt Numbers for

Capacitor No. 1, e = 0.50 63

X. Temperature-Time Data for Capacitor No. 1, e = 1.0 .. 6k

XI. Data for Computing Reynolds and Nusselt Numbers for Capacitor No. 1, e = 1.0 65

XII. Temperature-Time Data for Capacitor No. 2, e = 0 . . 66 XIII. Data for Computing Reynolds and Nusselt Numbers for

Capacitor No..2,. e •= 0 . . . . . . . . . . . . . . . . . 67

v i i i

LIST OF SYMBOLS

a, a"*" - constants

p

A - surface area of the capacitor, f t

C - heat capacity of the capacitor, Btu/F

0^ - specific heat of a i r , Btu/ lb . F

C "*" '- specific heat of the capacitor, Btu/lb F

- heat capacity of the supporting p las t ic , Btu/F

D- - outer diameter of the inner cylinder, ft.,

LV> - inner diameter of the outer tube, f t k x flow area ,

D e - hydraulic equivalent .diameter, w e t t e d perimeter f t

k x flow area , D n -Nusse l t equivalent diameter, h e a t e d perimeter f t

e - eccentricity parameter

G - mass velocity, lb /hr f t

2 h - average heat transfer coefficient, Btu/hr ft' F

1^ - maximum velocity head, i n . of water

h s - stat ic pressure head, i n . of water

h w - pressure drop across or i f i ce , i n . of water

K - thermal conductivity of f l u i d , Btu/hr ft F

- thermal conductivity of plast ic support, Btu/hr f t F

Kg - thermal conductivity of capacitor material, Btu/hr f t -F

1 m, m - constants

constants hDe

~K - Nusselt number,

I X

N - Prandtl number, • • 1

Pr

GDe

W^e - Reynolds number,

r-j_ - outer radius of the inner cylinder, f t

r^ - inner radius of the outer tube, f t

r - radius at the point of maximum velocity, f t m

T - temperature of the capacitor at any instant, chart div.

T . - temperature of a i r , chart div. or F a

T Q - temperature of capacitor at zero time,.chart div .

T* - dimensionless temperature

V a V g - average flow velocity, . f t / h r

V m a x - maximum point velocity, f t /hr

w - mass of the capacitor, lb

9 • - time,. sec

A - slope, l / h r

- dynamic viscosity of a i r , lb /hr f t

^M.w - dynamic viscosity of a ir at the so l id wall , lb /hr f t

^ - density of a i r , l b / f t

'XQ - time constant of the capacitor,.sec

. - time constant of the instrument, sec

- functions

1

CHAPTER I

INTRODUCTION

The purpose of this investigation was to measure the heat

transfer coefficients in.an annulus formed by placing a smooth cylinder

at various positions inside a c ircular tube with f l u i d flowing tur-

bulently along the longitudinal axis of the cylinder. The heat flow

was through the inner cylinder surface and the variations of heat

transfer coefficients due to different positions of the inner cylinder

were studied. The investigation was l imited to the Reynolds number

range from 15,000 to 65,000.

This problem is of interest because of developments in the

peaceful uses of atomic energy which necessitates a knowledge of heat

transfer coefficients i n certain types of odd-shaped flow passages.

In the present designs of heat exchangers and nuclear reactors, the

coolant flows in longitudinal passages formed by the spaces between

para l l e l rods or tubes in* closely spaced arrays within a cy l indr ica l

container. In gas cooled nuclear reactors, arrays of fuel bearing

rods are cooled by gas flowing para l l e l to the longitudinal axes of

the rods. This general configuration provides increased heat transfer

surface to compensate for the reduced heat transfer coefficients as­

sociated with gaseous flows. This type of flow geometry has received

very l i t t l e attention from research workers. This has resulted i n

the use of heat transfer coefficients in design which are not always

safe and accurate. An experimental programme was undertaken for the

very simplest case of this geometry, namely an annular cross-section.

2

The usual method of determining the heat transfer coefficients

requires the measurement of the temperature of the heat transfer me­

dium, and of the heat, transfer surface under steady-state conditions.

It is. d i f f i c u l t to measure the,surface temperature accurately so that

steady-state methods require elaborate apparatus and instrumentation.

To obviate these d i f f i cu l t i e s a non-stationary method has been used i n

this investigation. This method, the transient heat transfer test

technique ( l )* is based on the cooling.of a body having fixed thermo-

physical properties under a step-change of temperature. The under­

lying theory of this technique w i l l be discussed i n . d e t a i l in the next

chapter.

Using this technique results were.obtained .for heat transfer

in the concentric annulus. These results were compared with correla­

tions given by Wiegand (2) and Monrad and Pelton (3). Results for the

eccentric annulus were also obtained in a similar manner. These lat ter

results are of interest because of the paucity.of data for the eccen­

t r i c annulus.

DEFINITIONS OF TERMS USED

Annulus An annulus is defined as the flow passage formed by

placing a cy l indr ica l core inside a c ircular tube with f l u i d flowing

along the longitudinal axis of the core. When the cy l indr ica l core is

at the centre of the outer tube the resulting flow cross-section is

termed a concentric annulus. • An eccentric annulus is formed by placing

the core cylinder at positions other than the centre of the outer, tube.

* Numbers in parentheses refer to bibliography at the end of the Thesis.

3

Thermal Capacitor The heated so l id body used in.the exper­

iment is cal led the thermal capacitor cylinder. For the sake.of bre­

v i ty in the subsequent chapters this w i l l be cal led the capacitor.

REVIEW OF LITERATURE ON ANNULI

Concentric Annulus A large number of experiments has been

carried out on heat transfer in turbulent flow in a concentric annulus.

Most investigators attacked the problem by dimensional analysis and

presented equation basical ly of the form,

m n D %u - a (%e) ttpr) 01 C^) — - [ l ]

hD e

where, N|gu = Nusselt number, • -—

GD e . 1 L 0 = Reynolds number, —— ite ^/\A

Np , = Prandtl number, ^~

a, m.and n are constants which were determined experimentally.

This equation is of the same form as that for conduit flow,

1 1 / D 2

%u = a (%e)m ( N P r ) n > w i t h t h e addition of the term, 011 ^

to include the dimensional characteristic of the annulus.

Jordan (2U), i n 1909> studied the heat transfer from the

inner wall of two ver t i ca l annuli of different dimensions. The annuli

were formed by placing a copper pipe inside a cast iron casing. The

diameter ratios were 1.25 and 1.^7• A ir at temperatures varying from

2^0 F to 700 F was passed through the inner tube and water at

temperatures up ."to 200 F was circulated through the annular space. The

test section was hO f t . long and i t was placed direct ly after an elbow.

The experimental results covered a Reynolds number range from-7,000 to

95 ,000 .

Thompson, and Foust ( 25 ) , in 19^+0, investigated the heat

transfer characteristics in two double-pipe heat exchangers. One of

them was made of one inch pyrex tubing jacketed with two inch iron pipe;

the other was two inch pyrex tubing i n a three inch pipe. Cold water

at 50 F to 95 F flowed through the annular space and :sfceam.!. was con­

densed at the inner pyrex tube. The test section was 10 f t . long and

was placed direct ly after an elbow. The heat transfer, coefficient was

determined from the overall resistance by assuming that the coefficient

was a function of water velocity in the annulus only. The experimental

data was taken at Reynolds number greater than 100,000.

Foust and Christ ian ( 4 ) , i n the same year, investigated the

heat transfer coefficients i n annuli having various thicknesses of the

annular passage. The annulus was formed by assembling thin walled;,

copper tubing inside standard iron pipe. The diameter rat io ranged

from 1.20 to 2 . 5 6 . Water flowed through the annular space and steam

was condensed inside the copper tube. The test section was 8 .66 f t .

long with no provision for a calming section. The heat transfer coef­

f ic ient was calculated by graphical dif ferentiat ion. The investigation

covered a Reynolds number range from 3>000 to 60 ,000 . Thet equation

recommended was,

? . . . o < ? ) " fc)" (1) H

5

This equation was based on,Nusselt's equivalent diameter, D n defined

as,

D _ h x Flow area n Heated Perimeter

The authors also found.that the results could be correlated by using

the conventional equivalent diameter, based on the wetted perimeter,

by the following equation,

* - « ( J ) " ( j) H

Zebran (26) i n the same year also studied the heat transfer

characteristics at the inner wall of an annulus. The•core cylinder

was e l ec tr i ca l ly heated and a ir was forced through the annular passage.

Five different diameter ratios were used ranging from-.1.18 to 2.72.

Provisions were made for a calming-section which varied between 8 and

125 equivalent diameters. The heat transfer coefficients were ca l ­

culated by measuring the core wall temperature and the temperature of

the a ir stream. The experimental data covered the Reynolds number

range from 2,600 to 120,000.

. Monrad and.Pelton (3) i n the same year presented experimental

results of heat transfer coefficients i n three different annuli with

two different f luids flowing i n turbulent flow. The diameter ratios

were I.65, 2.^5 and 17 for heat transfer from.inner wall , and I.85 for

heat transfer from outer wal l . The test section.was 6.5 f t . long with

a calming section at the entrance. The investigation covered a

Reynolds number range from 12,000 to 220,000. The experimental data

6

for heat transfer at the inner wall were correlated.by the equation,

• / \ ° - 8 / \ n / \ 0.53

where n = O.h for heating and.0.3' for cooling. The properties were

evaluated at the main stream temperature. It was also suggested, on

the assumption that the relative skin f r i c t i o n on the two s'urfaces was

the same for turbulent as for laminar flow, that the constant term,

AM 0 - 5 3

0.02 I — I , i n equation |_UJ could be modified for better ac-

+ n o « l 21n D 2 / D l - ( D2 / D l ) 2 + 1 curacy to 0.023 [ ' *—' : D2/Dx - D X/D 2 - 2(D 2 /D X) I n D 2 / Y ) ±

It is to be noted here that the agreement between the equa­

tions of Foust and Christ ian, and Monrad and Pelton is very poor. As

Barrow (5) pointed out, for diameter ratios 16 and 2.k respectively,

the former investigators predict results 6.0 times and 2.2 times

greater than those predicted by the lat ter investigators.

Mueller (6), also in the same year, investigated heat trans­

fer from a fine wire placed inside a tube. This was a very special

case of annuli because with such a small core and large thickness of .

annulus a combination of cross flow and para l l e l flow is l i k e l y to

exist . Therefore, his correlations could not be compared with an

annulus of the proportion used in this investigation.

Davis (7), i n 19 3, presented another equation for heat trans­

fer from inner.wall with turbulent flow of f lu ids . The equation was

obtained by dimensional analysis and was valid for diameter ratios

from 1.18 to 6,800. The suggested equation was,

. / \ 0.8 / x 1/3 , v 0.1k' , x 0.15

The constants i n this equation were determined by comparison with the

experimental data of other investigators.

McMillen and Larson (27), i n 19kk, obtained annular heat

transfer coefficients i n a double pipe heat exchanger. The test

section consisted of four passes having different annular spaces with

brass or steel tube placed inside a standard iron pipe. The diameter

ratios were 1.245', 1-3, 1.532 and 1-970. The length of the test.sec­

tion.was 11 f t . There were no calming sections at the entrance of

each pass. The coefficients were calculated by assuming that a l l the

thermal resistances except that of the film were constant. The ex­

perimental data covered a Reynolds number, range from 10,000 to 100,000. The best correlation of data was given by the equation,

= 0.0305 —- [6]

Wiegand (2), i n 19 -5, made a detailed study of a l l the ex­

perimental data on heat transfer from the inner wall. The best cor­

relation f i t t i n g these data was found to be,

The equation was va l i d for Reynolds number greater than 10,000 where

the properties were calculated at the bulk temperature.

8

Apart from dimensional analysis, this problem has also been

attempted by establishing an analogy between f l u i d f r i c t i o n and heat

transfer. In 1951> Mizushina (10) investigated this approach but the

analysis was quite d i f f i c u l t due to lack of similarity between the

velocity and temperature profiles when heat was flowing from .the inner

wall only. Using' many assumptions Mizushina derived an equation for

the heat transfer coefficient which was very complicated for general

use. Barrow ( l l ) , i n 1961, presented a semi-theoretical solution by

considering the transfer of heat and transfer of momentum. The sol­

ution was applicable for fluids having a Prandtl number equal to

unity.

Eccentric Annulus Heat transfer i n eccentric annuli has

received very l i t t l e attention. Deissler and Taylor ( l 2 i ) , i n 1955>

made a theoretical analysis of f u l l y developed turbulent heat transfer

i n an eccentric annulus. It was found that the average Wusselt number

decreased as the eccentricity of the inner tube was increased. It was

also shown that the Wusselt numbers for a concentric annulus were

sli g h t l y higher than those for a tube with an equivalent diameter.

In 1962, Leung, Kays and Reynolds (13) presented heat

transfer data i n concentric and eccentric annuli based on a theoret­

i c a l study as well as an experimental investigation. For the eccentric

annulus the diameter ratios ranged from 2 .0 to 3»92 and for the con­

centric annulus from 2 .0 to 5»2. Air was flowing through the annulus

under f u l l y developed turbulent flow conditions. The experimental

results covered a Reynolds number range from 10,000 to 150 ,000.

9

CHAPTER II

THE TRANSIENT TEST TECHNIQUE

The transient heat transfer test technique as used in this

investigation has also .been used by other investigators in different

types of flow situations. London, Boelter and Nottage ( l ) proposed

this method i n 19^1, Eber (l^) used this method to obtain.data on heat

transfer characteristics i n superonsic flow over cones, and Fischer

and Norris (15) determined the convective heat transfer coefficient

by an analysis of skin temperature measurements on the nose of a V-2

rocket i n f l i g h t . In the past decade Garbett (16) used the transient

technique to determine the heat transfer coefficient from bodies i n

high velocity flow. Kays, London and Lo (l?) demonstrated success­

f u l l y i t s usefullness in determining the heat transfer coefficient

for gas flows normal to tube banks.

•Basical ly the transient technique for determining heat

transfer coefficient consists i n establishing an i n i t i a l temperature

potential between the f l u i d and the body by heating.or cooling, then

observing and recording the temperature-time history of the body as i t

returns towards equilibrium with the f l u i d stream. The heat transfer

coefficient is calculated from this record.

The simplest case of transient heating or cooling of a body

i s one i n which the internal resistance of the body is negligibly

small i n comparison with the thermal resistance of the sol id-f luid ,

interface. This is because such a system permits the lumping of a l l

the resistances to heat transfer at the boundary of the so l id body.

10

This ideal i sat ion. i s based on the assumption that the material of the

capacitor has i n f i n i t e l y large thermal conductivity. .Many transient

heat flow problems can be solved with' reasonable accuracy by assuming

that the internal conductive resistance is so small that the temper­

ature throughout the body is uniform at any instant of time.

A quantitative measure of the relat ive importance of the two

resistances can be expressed by a dimensionless modulus, cal led the

Biot number> which is defined as,

= B L KS

where, h = surface coefficient of heat transfer

=- , , . . . , j . . Volume of the body L = a characteristic length, — — Surface area

K s = thermal conductivity of the body

As Kreii^h (l8) pointed out, for bodies whose shape resembles a plate,

a cylinder, or a sphere, the error introduced by assuming that the

internal temperature at any instant is uniform w i l l be less than 5 per

cent when the internal resistance is less than 10 per cent of the

external surface resistance. In other words this w i l l hold when

N B i < 0 . 1 .

Keeping in mind the above requirement, the capacitor of the

present experiment was made of copper which has one of the highest

thermal conductivities amongst the naturally available metals. For a

capacitor of this metal, the rate of temperature change w i l l depend

11

only on the average surface heat transfer-coefficient which varies

mainly with the f lu id properties, the flow conditions, and the flow

geometry.

The theoretical equation describing the energy balance on

the cooling capacitor under this idealised condition can be formulated

as,

The change of internal energy of the thermal capacitor dur­ing a small interval of time

-C dT = hA (T - Ta) d'9

The net heat flow from the thermal capacitor to the f l u i d stream during the same interval of time

where, C = heat capacity of the capacitor

A = surface area in contact with f l u i d stream

9 = time

T = temperature of the cooling capacitor at any 9

Ta = temperature of the f l u i d stream

The minus sign on the l e f t hand side in equation [_Q~]' indicates that

the internal energy decreased when T > Ta as was the case in this

experiment.

In solving equation [jf) , C, A and Ta are assumed constant.

For small variation of. T and constant flow, h w i l l be essentially

constant. The solution becomes,

T - Ta To - Ta exp

hA 9 03

12

where, To = temperature of the capacitor•at.9 = 0.

This equation can be rewritten in the following form,

log„ T* = I -r ~ ] 6 [10]

where, T* =

3e . \ • C

T - Ta To - Ta

If the assumption i s legitimate then a plot of l o g g T* as

the ordinate and. 9 as the abscissa would y ie ld a straight l ine the

slope of which w i l l be — From this slope the value of h can be

calculated.

DISCUSSION OF ASSUMPTIONS

In establishing and solving equation QjJ several assumptions

have been made. - A . c r i t i c a l evaluation of these assumptions is nec­

essary at this stage to support the appl icabi l i ty of the transient

test technique to heat transfer in annular flow.

1. The assumption involving the ideal isat ion that a l l re­

sistances to heat transfer are lumped at the so l id f l u i d interface

is the key point to the whole analysis. Accuracy requirements for a

given problem.determine whether or not this approach.is useful. In

most heat transfer experiments, results with an error of plus or minus

25 per cent may be considered very good. However, Kays,, London and

Lo (17) claimed that their experimental error was plus or minus 5 P e r

cent where they used a similar method for the cross-flow heat exchanger.

It is. expected that in the present experiment the error would be con­

fined to the same l i m i t .

13

2. Heat transfer is assumed to be by forced .convection only.

In a f u l l y developed turbulent flow free convection effects are almost

negligible. However, in viscous flow with a large'annular gap the

poss ib i l i ty of free convection effects cannot be to ta l ly ignored. . In

this experiment the flow conditions were always turbulent and therefore

free convection effects can be neglected.

It is also assumed that radiation effects are negligible.

For small temperature difference at low temperature leve l with pol ­

ished model surfaces this effect would be very small. But for high

temperatures, radiation loss can be significant which means that the

heat transfer coefficient as determined by this method would contain

a contribution f rom the radiation coeff icient. Temperatures of about

60 to 70 F above ambient can be considered low enough so as not to

cause any serious error due to radiation. The present experiment was

conducted in this range of temperature.

3• The temperature difference i n the radia l direction inside

the capacitor and i n the axial direction along i t s length is negl i ­

gible . This can be achieved by having a thermal capacitor of very high

thermal conductivity and re lat ive ly thin wall thickness.

k. Heat loss to the supporting structure of the model is

assumed very small. -As Garbett (16) noted in his investigation, the

mounting structure sometimes provide additional sources of heat loss.

For example, during a cooling process the capacitor cools much faster

than the supporting medium so that towards the end of the transient

cooling heat may flow from the supports to the capacitor. This effect

Ik

can be best-reduced .by keeping the area of contact between capacitor

and.support small and using supporting material having a small (K^C^)

product,

where, . = thermal conductivity of the supporting material

= heat capacity of the supporting material

5• The average value of the specific heat of the material

of the capacitor is constant. The specific heat of•copper is essen­

t i a l l y constant between temperatures-'70 to 150F. The mass of the

capacitor is also constant;, and therefore the heat capacity is

constant.

6. The bulk temperature of the f l u i d stream is constant

during the test. To verify this a i r temperature was measured con­

tinuously at the outlet of the test .section for the duration of one

..complete run. It was found that the variation was not more than 1 F

which was less than 1.5 per cent of the ambient temperature.

15

CHAPTER III

APPARATUS

The apparatus was designed to measure the following:

(a) the a ir flow rate

(b) the temperature and pressure of a ir

(c) the temperature-time history of the capacitor

Two different arrangements of apparatus were used. One for

the study of the concentric annulus and another for the eccentric

annulus. In Figure 1, a schematic layout of the apparatus used for

the concentric annulus is. shown. The arrangement consisted of a test

section, a mixing box and a centrifugal blower. The test section,

shown in Figure 2, was made of transparent plast ic outer tube having

an inside diameter, Uq = 3 i n . , and a wall thickness of l/k i n . The

inner cylinder on which the capacitor wasi mounted had an outside dia­

meter, = 1 i n .

Air at room temperature was blown through the test section

by a l/3 hp centrifugal type blower with a speed rating of 3^50 rpm.

The a i r flow rate was determined by measuring the maximum velocity in

the annulus by a pitot static tube placed at the downstream end of the

test section and connected to a micro-manometer.

A mixing box between the blower and the test section acted

as a surge tank and tended to smooth pulsations in the a ir stream.

16

The temperature variation of the cooling capacitor was

measured by a copper-constantan thermocouple connected to an .automatic

recorder to obtain a temperature-time history.

The apparatus'" used for the eccentric annulus test is shown

schematically in Figure 3« The same test section and mixing box were

used i n this arrangement but a higher capacity blower was used to

allow an or i f i ce meter to be used for measuring a ir flow. In the ec­

centric annulus the a ir flow rate could not be determined by pitot tube

as in the case of concentric annulus because of the non-symetrical.

fom of velocity prof i le in an eccentric annulus. The flow rate was

therefore measured by a f la t plate, square edged or i f ice placed up­

stream of the test section. The large pressure drop across the or i f ice

required the higher capacity blower to cover the same range of Reynolds

number as was obtained in the concentric annulus flow. A detailed

description of the two a ir metering systems i s given i n Appendix I .

The blower used in the second arrangement was a 3/h hp

centrifugal type blower with a speed rating of 3^50 rpm. A i r temp­

erature was measured by a mercury in.glass thermometer graduated to

1 F and also by a copper-constantan thermocouple placed in the mixing

box. The change i n the flow Reynolds number was accomplished by

thrott l ing the a ir flow at the in le t side of the fan.

The length of the test section was selected to give a f u l l y

developed hydrodynamic flow. There is s t i l l a considerable doubt as

to the exact length after which the flow is f u l l y established in an

annulus. One group of investigators, M i l l e r , Byrnes and Benforado (19)

17

claimed that i n a concentric annulus the velocity prof i le is establish­

ed i n twenty equivalent diameters. In the present investigation, this

figure was taken as the design cr i ter ion to select the length of the

test section. It was also found that there was no re l iable information

available as to the entry length required for the establishment of a

f u l l y developed flow in an eccentric annulus. However, i t was assumed

that the entry length.in both concentric and eccentric annuli was of

the same order of magnitude.

The heat transfer characteristics of the capacitor was

studied by recording i t s temperature-time history during a transient

cooling period. Two capacitors were used. The f i r s t one, shown in

Figure 2, was 2.125 i n . long with an outside diameter of 1 i n . and an

inside diameter of.0.776 i n . The capacitor was made from so l id copper

rod d r i l l e d to the required inside diameter and faced to the desired

length. A small hole was d r i l l e d in the wall of the capacitor to

provide space for the thermocouple junction. In selecting the size

of the capacitor, care was taken to comply with t h e B i o t number re­

quirements and other assumptions made i n Chapter I I .

A second capacitor was made of the same material as the f i r s t

but was smaller i n length and mass. It was 1.1+703 i n . long with an

outside diameter of 1 i n . and an inside diameter of 0-7175 i n . Figure 2

shows the dimensions of this capacitor. A few tests were made with this

capacitor to show that the length of the capacitors had l i t t l e effect

on the results obtained. Further details of the comparison are given

in Chapter IV.

18

The capacitor was mounted in the test section at the down­

stream end of the inner cylinder. The mounting structure consisted of

two plast ic end pieces, one on each side of the capacitor. The plast ic

sections had the same outside diameter as the capacitor so that f i n a l

assembled form has a smooth outside surface. For the concentric

annulus the remaining length of the, inner cylinder, upstream of the

capacitor, consisted of a so l id plast ic rod having an outside diameter

of 1 i n . Any small deflection due to the weight of the rod could be

ignored considering the large thickness of the annular passage. But

in the eccentric annulus, especially when the inner cylinder was

closer to the wall of the outer tube, any small deflection would cause

distortion i n the flow pattern. To minimise this effect the inner

cylinder was madeiof thin walled aluminium tubing: .with plast ic end

pieces to allow for the mounting of the capacitor. The overal l de­

f lect ion of the-aluminum tube was less than 0.010 i n .

Supports at the two ends were used to position the inner

cylinder within the tube. To al ign the tube accurately, templates were

• made from aluminium' plate. These templates had an outside diameter

of 3 i n . • with an one inch hole made at the required eccentric i t ies ,

namely, e = 0, e = 0.25 and e = 0.50. Having aligned the cylinder

with these templates, two thin metallic spiders crossing at right

angles were placed at the two ends of the cylinder. Right angled

grooves were made, at both ends of the inner cylinder to locate the

spiders; The inner cylinder with the spiders was then easi ly s l i d

into the outer tube. The same procedure was followed for the eccentric

annulus but in this case the l ine of intersection of the two spiders

RECORDER

MICRO-MANOMETER

PIG. 1. SCHEMATIC LAYOUT OP THE CONCENTRIC ANNULUS TESTS' H

^PLASTIC END PIECESN

4 r

?0

r

PLASTIC FOR CAPACT1

4 r

?0 rso.-ij e a 0 CAPACITOR

1.5

- — V

ALUMINIUM TUBE FOR ALL OJT-HER RUNS 2.0 2.1250 FOR #1 1.5 * it v

'l.4703 FOR #2 '

SUPPORTING ROD FOR CAPACITORS

1.0

2.1250

d.

CAPACITOR NO. 1

HERMOCOUPLE HOLE

0.7

1.4703

! THERMOCOUPLE HOLE

CAPACITOR NO. 2 NOTE! ALL DIMENSIONS IN INCHES

FIG. 2. TEST MODELS AND MOUNTING STRUCTURES ro o

RECORDER

ORIFICE7 THERMOMETER THERMOCOUPLES

/FLOW SCREEN THERMAL CAPACITOR-

FLOW

TEST SECTION 44.50 i n .

MANOMETERS

FIG. 3. SCHEMATIC LAYOUT OF THE ECCENTRIC ANNULUS TESTS

TEST SECTION SHOWING SUPPORT AT ONE END. OTHER END SIMILAR

SECTION A-A

4. METHOD OP SUPPORTING INNER TUBE FOR e = 0

(a) PHOTOGRAPH OP TEST SECTION

(b) PHOTOGRAPH OP CAPACITORS

PHOTOGRAPHS OP TEST SECTION AND CAPACITORS

2k

was shifted to give the desired eccentricity of the inner cylinder.

The supporting device for the concentric annulus is shown i n Figure k.

Photographs of the test section and the capacitors are shown i n

Figure 5•

INSTRUMENTATION '

As mentioned i n the earlier chapter, the heat transfer co­

efficient was determined from a record of the temperature-time history

of the cooling capacitor. Since the temperature of the capacitor was

decreasing with time, a measuring probe capable of fast response to

a changing temperature was desired. An ideal temperature measuring

probe would f a i t h f u l l y respond to any change regardless of the time

rate of temperature change of the capacitor. The thermocouple was

the obvious choice for this type of measurement because of the f o l ­

lowing reasons:

.' The time constant of the thermocouple wire i s a function of

the ratio of heat.capacity to i t s surface area. The thermocouple

junctions have small mass and hence small thermal capacity. The area

of contact is comparatively large due to soldering of the probe to the

capacitor. Therefore, the thermocouple wire has a small time constant

and follows closely any temperature variation i n the capacitor.

In the range of the experiment, which was from 70 to 1^0 F,

the electro-motive force of the thermocouple is practically a linear

function of the temperature. Thus i t was possible to plot the dimen­

sionless temperature T* in equation N-Ol i n terms of the emf difference

25

instead of the temperature difference. This simplified not only the

computation but also the cal ibration of the recording instrument.

The copper-constantan thermocouple used for measuring the

capacitor temperature and the a ir temperature in the mixing box was

26 gauge B & S, so l id wire with polyvinyl insulation.

The temperature-time variation of the capacitor was recorded

on, the chart of a B r i s t o l recorder. The range of the recorder was

adjusted to 0 to 2.5 mi l l ivo l t s and the chart speed was kept constant

at 3/8 in . .per min. It was believed that the Br i s to l recorder had a

faster response than that of the capacitor so any error due to instru­

ment lag was negi l ig ib le . A quantitative estimate of the relat ive

error w i l l "be presented in the discussion of results , Chapter XV.

This error, according to Garbett (l6), i s the rat io of the instrument

time constant to the capacitor time constant.

Two thermocouples were used i n the experimental arrangement

with a selector switch to connect one thermocouple to the recorder

at any one time. A schematic diagram of the thermocouple c i rcu i t with

related instrumentation is shown in Figure 6.

26

r

V

REP. JUNCTION 32 P

.JUNCTION BOX

COPPER

: CONSTANTAN T -T.C. TO CAPACITOR T a -T.C. TO MIXING BOX

.SELECTOR SWITCH

BRISTOL RECORDER

PIG. 6. THERMOCOUPLE CIRCUIT

27

CHAPTER IV

EXPERIMENTAL PROCEDURE

For each set of experiments the inner tube was f i r s t aligned

to the particular eccentricity for which the test was to be made. The

capacitor was then heated to 60 to 70 F above the ambient temperature

by an external heat source consisting of an e lectr ic soldering iron

with an aluminium extension piece to reach the capacitor inside the

tube. The heat source was then withdrawn, the recorder and the a ir

fan motor switch were turned on. As the capacitor was cooling towards

equilibrium in the f l u i d stream, a continuous record of temperature

against time was made in the recorder. This record was taken for .

approximately 130 seconds. The selector switch was then turned on to

the a ir temperature thermocouple and a record of this temperature was

also made on the same chart. About the middle of each run; or i f i ce

pressure drop, static pressure and temperature of a ir at the in le t

side of the or i f ice and the a ir velocity were recorded. When one

test was complete, the flow.rate was changed by thrott l ing the a ir at

the in let to the fan. The same procedure was then repeated t i l l a

Reynolds number range from 15,000 to 65,000 was covered. A tota l of

about 13 to 16 runs were taken for each position of the annulus.

Four positions of the annulus were investigated. Each posi­

t ion was designated by the eccentricity parameter, e, defined by the

following•relation:

e _ Distance between the centres of the two cylinders r2 " r l

28

The four positions were thus, e = 0, e = 0.25, e = 0.50, and e = 1.0.

PRESENTATION•OF RESULTS

The temperature time history of the capacitor as obtained

for a typical run is shown.in Figure 7. For the purposes of comp­

utation a l l the.experimental data were entered in tables; given in

Appendix V. The f i n a l results have been presented in graphical form

with dimensionless parameters on log-log co-orindates. This presenta­

tion was of the following form:

NNu = i 2 S

2 ( W Re)

In the present experiment, the a ir was at room temperature

which at times varied between 70 F and 90 F . The Prandtl number for

a ir i n this temperature range is pract ica l ly constant. Therefore,

a log-log plot of Nusselt numbers as a function of Reynolds numbers

only have' been presented.

In Figure 8, the variation of Nusselt number with Reynolds

number has been shown for an annulus with eccentricity parameter equal

to zero. In the same sheet equations of other investigators such as

Wiegand (2), Monrad and Pelton (3) and Foust and Christ ian (k) have

also been plotted.

The results of the eccentric annulus for three different

eccentricity parameters, e = 0.25, e = 0.50 and e = 1.0 are shown i n

Figures 9> 10 and 11 respectively. In each case, the best l ine

correlating the data.is also shown.

29

-o =e— p 1

,—1

_ "

0 0 0

hi n n n

r.t o O o

ri n n

f* a o o

rti o o O

;

( , r> o -

T m

o S 5

n n

7?

C a w No. R5000 5 QlMI_J> CHUT No. RSOOO 8 l_lu3Z CHUT No. RSOOO O [ZSB

PIG. 7. A TYPICAL TEMPERATURE-TIME RELATION AS OBTAINED ON THE RECORDER

30

&5

tt w pp

E-i H i W CO ra &5

300

270

240

210

180

150

120

90

60

30,

WIEGA

iND CHRISTIAN

)

/ ^ ^ ^ ^

^MONRAD AND I 'ELTON

REYNOLDS NUMBER, N R E

FIG.. 8. HEAT TRANSFER AT INNER WALL OF ANNULUS, e = 0

31

300

270

240

210

60

1.3xl0 4 2 3 4 5 6 7xl0 4

REYNOLDS NUMBER, N R e

pIG. 9. HEAT TRANSFER AT INNER WALL OF ANNULUS, e = 0.25

32

300

270

240

210

180

60

1.3xl0 4 y 2 3 4 5 6 7xl0 4

REYNOLDS NUMBER, N R

PIG. 10. HEAT TRANSFER AT INNER WALL OP ANNULUS, e = 0.50

33

300 •

270 •

240 •

210 •

180 -

150

1.3x10* 2 3 4 5 6 7x10 REYNOLDS NUMBER, N R e

PIG. 11. HEAT TRANSFER AT INNER WALL OP ANNULUS, e =1.0

3^

In Figure 12, the variat ion of Nusselt number with Reynolds

number and eccentricity parameter is shown. It is interesting to note

that the average Nusselt number decreased with increasing annulus

eccentricity. In•Figure 13, this decreasing trend of Nusselt number

with eccentricity parameter has been plotted for a fixed Reynolds

number.

DISCUSSION OF RESULTS

This section includes a discussion of a l l the experimental

results and an evaluation of the probable errors involved in different

parts of the investigation.

Experimental data for the average heat transfer coefficient

in a concentric annulus are shown in Figure 8. Since a l l these data

were obtained in almost isothermal condition, the Prandtl number of

the a ir was always constant. The equations of Wiegand, Qi-J of

Monrad and Pelton and of Foust and Christ ian are plotted in the

same sheet to compare the experimental results . It is noted that the

agreement is very good indeed with equations (V) and QJ-J . The

equation of Foust and Christ ian predicts much higher values of heat

transfer coefficients although the trend shown is the same. .Foust and

Christ ian obtained their water side coefficients by means of a semi-

graphical method which resulted in steam coefficients which were very

high so that their results have been questioned by latter investigators

(5, 21).

The equation Qjf} of Davis (7) was not considered a proper

comparison with the present data because i t is based on the inside

35

270

240

o e = 0.0

• e = 0.25

A e = 0.50

O e = 1.0

1.3x10* 2 3 4 5 6 7x104 REYNOLDS NUMBER, N R -

PIG. 12. VARIATION OP NUSSELT NUMBER WITH REYNOLDS NUMBER AND ECCENTRICITY PARAMETER

0.0 0.25 0.5 0.75 1.0 ECCENTRICITY PARAMETER, e

PIG. 13. VARIATION OP HEAT TRANSFER COEFFICIENT WITH INNER TUBE ECCENTRICITY

37

diameter of the annulus. Davis agreed that when heat transfer occured

only at the inner surface the use of inside diameter in the Nusselt

and Reynolds numbers was reasonable. However, as Barrow (5) pointed

out the computation of Reynolds number based on the inside wall d ia­

meter can in no way be considered as a measure of the kind of flow..

Also the f r i c t i o n in annuli results from resistance at both the inner

and outer wall of the annulus. Therefore, the most reasonable defin­

i t i o n of Reynolds number is the one based on the conventional equi­

valent diameter, D e .

The heat transfer coefficients presented here are claimed

to be the average value in a f u l l y developed turbulent flow. A

question may arise as to the v a l i d i t y of this statement on the grounds

that the thermal boundary layer was not completely developed in the

length of the capacitor. As mentioned in Chapter II the transient

technique does measure the average heat transfer coefficient, provided

a l l assumptions have been sat is f ied. To just i fy this statement a

second experiment was carried out for the same annulus but with a

capacitor of different length. Capacitor No. 2 was thus designed with

a length of I.U703 i n . thereby having a reduction in length of 30

per cent of that of Capacitor No. 1. Figure 2 shows the details of

the second capacitor. The heat transfer data obtained by using both

these capacitors are plotted in Figure lh. The good agreement be­

tween these results indicates that the earl ier statement was reasonable.

Kays, London and Lo (17) pointed out that the transient

technique is not adequate for laminar flow because of the tendency

38

fe

fe

EH

CO

•B

300

270

240

210

180

150

120

90

60

30

C o r> )

di ii

c

>

o

o •

0 •

!

/

i O CAP

• CAP

ACITOR N

ACITOR N

0. 1

0. 2

7x10 REYNOLDS NUMBER, N R e

PIG. 14. COMPARISON OP HEAT TRANSFER DATA OBTAINED BY CAPACITORS NO. 1 AND NO. 2

39

of the temperature prof i le to extend completely across the flow

stream rather than being confined to a re la t ive ly thin boundary

layer such as in turbulent flow. This is why the transient technique

gives' the average values of heat transfer coefficients provided the

flow is f u l l y turbulent. In addition, the results shown in Figure 8

also suggest that the data obtained in . th i s investigation are the

average heat'transfer coefficients.

Refering to Figure 8 again, i t may be noted that the ex­

perimental, point at the lowest Reynolds number tends to be higher

than that predicted by the equations of Weigand and Monrad and

Pelton. It i s believed that at very low Reynolds number the cooling

rate of the' capacitor becomes very slow and hence towards the end of

the cooling period the capacitor is l i k e l y to loose heat to the sur­

rounding supports at each ends. At higher Reynolds number this loss

is negligible because the capacitor cools very quickly.

In Figure 12, the variation of heat transfer coefficient

with Reynolds number and eccentricity parameter is shown. It was

found that the average Nusselt number decreased as the eccentricity

was increased. This trend is in. good agreement with Deissler and

Taylor's (12) theoretical analysis. The best l ine f i t t i n g the data

has also been drawn in each case and i t is noted that the slope of

the lines is nearly constant for a l l eccentricit ies of the annulus.

It was observed that the tota l decrease in Nusselt number was 36 per

cent at the highest Reynolds number and about 1+0 peri.cent at the

lowest Reynolds.number. . Figure 13, shows this variation at four

^0

different Reynolds number. The rate of decrease of heat transfer co­

eff icient was found to be greater within the f i r s t 50 P e r cent of

the eccentricity. Between 50 and 100 per cent eccentricity the var­

iat ion of heat transfer coefficient was much.less.

It was pointed out i n Chapter II that in the solution of

equation (V) the heat transfer coefficient and the heat capapcity of

the test model were assumed constant. Considering the fact that the

semi-log plot of equation [loj from the experimental data followed

the expected straight- l ine relationship, these assumptions seem to

be jus t i f i ed . A typical semi-log plot of •equation (jLOj is shown in

Figure 15• However, any definite departure from the l inear relation

would necessarily make the above assumptions questionable. The con­

stancy of the heat capacity of the model w i l l depend on the variation

of the specific heat of copper with temperature. The temperature range

in the present investigation was between 70 F and ikO F . It is believed

that the variation of specific heat i n this temperature range was neg­

l i g i b l e .

The instrument lag effect may cause an error in the measure­

ment of heat transfer coefficient especially when the data recorded

were those of a transient state. As mentioned in Chapter III , the

relat ive error in the calculated value of the heat transfer coeff i ­

cient is given by the following relat ion:

Relative error = -— x 100 per cent -c

i l l

0.4

0 10 20 30 40 50 60 70 TIME, 9 (sec)

PIG. 15. TYPICAL SEMI-LOG PLOT OF DIMENSIONLESS TEMPERATURE WITH TIME

k2

w h e r e , = time constant of the recording instrument.

T c = time constant of the capacitor model.

The time constant of the recording instrument was obtained by apply­

ing a step change in the input. This was found to be 2.5 sec. The

time constant of the capacitor was given by the inverse of the slope

of the semi-log plot shown in Figure 15. The lowest time constant of

the capacitor during the entire experiment was that of Capacitor No. 1

during Run 13• This was found to be 9^-5 sec. Therefore, the maximum

relative error was 2.67 per cent.

In Chapter II itwas assumed that the temperature gradient

,inside the capacitor was negligible. When the annulus was concentric

this assumption was va l i d but one may question that this may not be

the case especially when the annulus was at the maximum eccentricity,

i . e . , the inner tube was touching the outer tube. An experimental

check was therefore made for the position e = 1.0 by placing the

thermocouple at three different points — a, b and c shown in

Figure l6 below. At one particular flow condition the maximum

variation in temperature between any of the above three points was

found to be less than 3 psr cent.

a

FIG. 16.

h3

The deflection or sag of the inner cylinder could cause an

error in the transient cooling of the model. When the annulus was

concentric any small sag in.the inner cylinder could not appreciably

influence the flow pattern because of the re lat ive ly large annular

thickness. Also the capacitor was mounted near the downstream support

'so.that any small sag was around the middle of the test section which

has much less influence on the capacitor. For the eccentric annulus,

however, the effect, of the sag', of the inner cylinder could be apprec­

iable especially at higher eccentricity. To avoid this a hollow alum-

i inium tube was used to support the capacitor i n the eccentric annulus.

This is shown i n Figure 2. The tota l deflection in the centre of

the tube was, in this case, l imited.to 0.010 i n . which is 10 per cent

of the maximum annulus thickness. It was assumed that this tolerance

was within the required accuracy of the experiment.

The errors due to cal ibration of the recording instrument

and also of the thermocouples were not considered to be of any con­

sequence. The experiment was conducted i n a small temperature range

and i t was.found that within this range the•temperature-emf response

of a copper-constantan thermocouple was very close to l inear . There­

fore, in the dimensionless temperature-time plot , Figure 15, i t was

sufficient to plot the logarithm of the emf ratios d irect ly from.the

recorder chart. Also because of the dimensionless temperature, the

cal ibration of the recording instrument was not required as long as

i t demonstrated a l inear scale.

1+1+

CHAPTER V

CONCLUSIONS

1. The use of the transient test technique was found to

be a simple and quick method for determining the heat transfer chara-

ter i s t i c s in an annulus. Heat transfer coefficients in an eccentric

annulus were found to decrease with increase i n eccentricity. The

decrease of heat transfer coefficient did not seem to be l inear ly

•related to the increase of eccentricity. However, the effect of

eccentricity was more pronounced in the range 0 e <0.5 where the

value of heat transfer coefficient decreased considerably. For

example, at Reynolds number of 50,000 approximately 67 per cent of

the to ta l decrease occured i n the range 0 ^ e <0.5 while the other

33 P e r cent occured in the range 0.5 ^ e ^1.0.

Equations of Wiegand (2) and Monrad and Pelton (3) were

found to correlate the annulus data of the present investigation very

well .

2. Almost isothermal data was obtained by the transient

method. In the annulus, the air temperature was pract ica l ly constant

for one complete: run. and therefore the evaluation of the properties

could be easi ly made at this temperature. This eliminates the trouble

of determining the f l u i d f i lm temperature required in other methods

of determining the heat transfer data.

3• The temperature of the cooling capacitor was measured

in an arbitrary scale during the experiment. Therefore, careful

1+5

cal ibration of the thermocouple and the recording instrument was not

required.

RECOMMENDATION FOR FUTURE WORK

The present investigation may be considered as an explor­

atory work for more extensive studies in the same f i e l d . One of the

important studies which is yet to be done is the behaviour of the heat

transfer coefficients in the region where neither the thermal nor

the hydrodynamic boundary layer has developed completely. This s i tua­

tion may be encountered in practice i n a reactor where the heat trans­

fer from the fuel rod is expected to take place from the very start

of the tube. This investigation can probably be made by using the

same technique provided a method is found to isolate the capacitors

thermally along the longitudinal direct ion.

BIBLIOGRAPHY

London, A. L . , Nottage, H. B . , Boelter, L. . .M. K. "Determination of Unit Conductances for Heat and Mass Transfer by the Transient Method" Ind. and Eng. Chem. V o l . 33, 19^1, P- 67

Wiegand, J . H. "Discussion on.Annular Heat Transfer Coefficients for Turbulent Flow by McMillen and Larson" Am. Inst. Chem. Engrs. Trans. V o l . i n , 191*5, p. U7

Monrad, C. C , Pelton, J . F . "Heat Transfer, by Convection in.Annular Spaces" Am. Inst. Chem. Engrs. Trans. V o l . 38, 19U2, p. 593

Foust, A . S . , Christ ian, G.A. "Non-boiling Heat Transfer in. Annuli" Am. Inst. Chem. Engrs. Trans. V o l . 30, 191+0, p. 5^1

Barrow, H. "Fluid Flow and Heat Transfer in an.Annulus with a Heated Core Tube" Proc. Inst. Mech. Engrs. V o l . 169, 1955, p. 1113

a

Mueller, A. C. . '!Heat Transfer from Wires to Air i n Paral le l

Flow " Am. Inst. Chem..' :Engrs. Trans. V o l . 38, 19^2, p. 613

Davis, E . S. "Heat Transfer and Pressure Drop in Annuli" Trans.•ASME V o l . 65, 19^3, P . 755

Knudsen, J . G . , Katz, D . . L . "Fluid Dynamics and Heat Transfer" McGraw-Hill Book Co. .Inc . 1958

Stein, R. P . , Begel, W. "Heat Transfer to Water in Turbulent Flow in Internally Heated Annuli" Am. Inst. Chem. Engrs. Jour:... V o l . k, 1958, p. 127

hi

(10) Mizushina, T. "Analogy between F lu id Fr i c t i on and Heat Transfer in Annuli" General Discussion on Heat Transfer - ASME/IME 1951, P. 191

(11.) Barrow, H. . "A Semi-theoretical Solution of Asymmetric

Heat Transfer in. Annular Flow Jour. Mech. Eng. Sc. V o l . 2 , i 9 6 0 , P . .331

(12) Deissler, R. G . , Taylor, M. F . "Analysis of Fu l ly Developed Turbulent Heat Transfer and Flow in.Annulus with Various Eccentric i t ies" NACA - TN 3U51, March, 1955

(13) Leung, E . Y . , Kays, W. M . , Reynolds, W. C. "Heat Transfer with Turbulent Flow in Concentric and Eccentric Annuli with Constant and Variable Heat Flux" NASA - N62 - 131V3, August, 1962

(lh) Eber, G. R. "Experimental Investigation of the Brake Temperature and Heat Transfer of Simple Bodies at Supersonic Speeds" Archiv. 6 6 / 5 7 , Peenemude, Nov., 19U1

(15) Fischer, W. W., Norris , R. H. "Supersonic Convective Heat Transfer Correlation from.Skin Temperature Measurements on a V -2 Rocket in Fl ight" Trans. ASME V o l . 71 , I9U9, p. ^57

(16) Garbett, C. R. 'The Transient .Method for Determining Heat Transfer Conductance from Bodies i n High Velocity

. F lu id Flow" Heat Transfer and F lu id Mechanics Institute Preprints of Paper, 1951 Stanford Univ. Press

(17) Kays, W. M . , London, A. L . , Lo, R.. K. "Heat Transfer and Fr i c t i on Characteristics for Gas Flow Normal to Tube Banks - Use of a Transient Test Technique" Trans. ASME V o l . 76, 195^, P- 387

(18) Kreith, F , "Principles of Heat Transfer" International Text Book Co. 1958

(19) M i l l e r , P . , Byrnes, J . J . , Benforado, D . M . "Heat Transfer to Water in an Annulus " Am. Inst. Chem.. Engrs. Jour. V o l . 1, 1955, P- 501

(20) ASME Power.Test Codes, Chap, 4, Part. 5

(21) Rothfus, R. R. "Velocity Distribution and F lu id Fr ic t ion in Concentric Annuli " D. Sc. Thesis, Carnegie Inst. Tech. 1948

(22) Stein, R. P . , Begell , Wm. "Heat Transfer to Water in Turbulent Flow in Internally Heated Annuli" Am. Inst. Chem. Engrs. Jour. V o l . 4, 1958, p. 127

(23) Giedt, W. H. "Principles of Engineering Heat Transfer" D. Van Wostrand Co. Inc. , 1958

(24) Jordan, H.P. "On the "Rate of Heat Transmission between F lu id and Metal Surfaces" Proc. Inst. Mech. Engrs. Parts 3 - 4 , 1909, p. 1317

(25) Foust, A. S. , Thompson, T. J . "Heat Transfer Coefficients in Glass Exchangers' Am. Inst. Chem. Engrs. Trans. V o l . 36, 1940, p. 555

(26) Zebran, A. H. 'Clar i f icat ion of Heat Transfer Characteristics of Fluids in Annular Passages" Ph. D. Thesis, Univ. of Michigan 1940

(27) McMillen, E . L . , . L a r s o n , R. E . "Annular Heat Transfer Coefficients for Turbulent Flow" Am. Inst. Chem. Engrs. Trans. V o l . 40, 1944, p. 177

h9

APPENDIX I

AIR METERING SYSTEMS

The a ir flow rate was measured to determine the Reynolds

number of the flow. The following two methods were used:

Method I . This method was used for Capacitor No. 1 at

eccentricity, e = 0. The a ir flow rate was calculated based on a

measurement of the maximum point velocity in the annulus. For laminar

flow i t has been shown that the radius at the point of maximum velo­

c i ty is related to the other r a d i i of a concentric annulus by the

equation:

r. m / 2 2 l o g e ( r 2 / r x ) =ex

Rothfus (21) has shown experimentally that the point of

maximum velocity for isothermal turbulent flow of a ir in a concentric

annulus was the same as that for laminar flow such as calculated from

equation [ l l ] . Later Knudsen and Katz (8) corroborated the same

fact with their experimental results . It has also been reported by

these authors that the turbulent flow velocity prof i le was very f la t

in the v i c i n i t y of the point represented by equation [ l l j . Knudsen

and Katz gave a relat ion of the average to the maximum velocity as

^avg/^max = ^ ^ T S with a diameter rat io of 3-6. In the present invest­

igation, however, the diameter rat io was 3>0. For this rat io Denton*

*Mech. Eng. Dept., Univ. of Br i t i sh Columbia, M.A.Sc. thesis in. preparation.

50

studied the velocity profi les in turbulent flow and concluded that

O.876 was correct for the present annulus. The average flow velocity

thus calculated had a maxiipum variation of 1.8 per cent.

The maximum point velocity was measured by a pitot static tube

placed at the radius, r m . It was mounted at the exit of the test sec­

t ion and was connected to an accurate micro^manometer capable of read­

ing low pressures from zero i n . of water head to 6.0 i n . of water head.

The temperature of the a ir stream was measured by an ordinary

mercury i n glass thermometer. The thermometer was graduated to 1 F .

It was found that the a ir temperature did not change appreciably dur­

ing this part-, of the experiment.

The Reynolds number was f i n a l l y calculated from the above data.

Method I I . This method was used i f o r the following cases:

1. Capacitor No. 1 at eccentricity, e = 0.25, 0.5 and,1.0.

2. Capacitor No. 2 at eccentricity, e = 0.

The a ir flow rate was determined using a f la t plate or i f ice mounted on

a 3 i n . schedule hO pipe. Figure 3 shows the position of the or i f ice

with respect to the test section and fan posit ion. The or i f i ce was

designed in accordance with ASME -.Power Test Code (20). Straight

lengths of eleven equivalent diameters at the in let and seven equiva­

lent diameters at the outlet of the or i f ice were provided as required

by the code. The flow coefficient was taken from the Table given in

the same reference. Table I gives the details of the o r i f i c e .

51

TABLE I. DETAILS OF ORIFICE

Pipe diameter, (in.) 3.068 O r i f i c e diameter, (in.) 1.628 Flow c o e f f i c i e n t 0.635 Pressure taps Flange taps M a t e r i a l S t a i n l e s s S t e e l

The o r i f i c e pressure drop and i n l e t side s t a t i c pressure of

a i r were measured by two ordinary U-tube manometers f i l l e d with dyed

water f o r be t t e r v i s i b i l i t y . The manometer scales were graduated i n

tenth of an inch. Since the ultimate objective was to determine the

flow Reynolds number, a small error i n the flow metering system was

u n l i k e l y to cause any appreciable error i n the f i n a l p l o t of the

r e s u l t s .

A i r temperature was measured by a mercury i n glass thermo­

meter graduated to 1 F.

52

APPENDIX II

PHYSICAL PROPERTIES AND CONSTANTS OF THE THERMAL CAPACITORS

The dimensional details of the two thermal capacitors are

shown i n Figure 3» The physical properties and constants of the cap­

acitors as required for the calculation of the heat transfer coeffits:"

cdentBc are given i n the following table.

TABLE II. PROPERTIES OF THE THERMAL CAPACITORS

Capacitor No. 1 Capacitor No. 2

Material Length, (in.) piameter, Dj (in.) Mass, (gm.) Cl (Btu/lb F) Kg, (Btu/hr F ft)

99-9$ Copper 2.1250 1.0

103.2312 0.0915

223.0

99.9$ Copper 1.4703 1.0

83.8931 O.O915

223.0

The calculated values of Blot number based on an average heat 2

transfer coefficient of 15 Btu/hr f t F are given i n the following

table. TABLE III. BIOT NUMBER OF THE CAPACITORS

Capacitor No. 1 Capacitor No. 2

N B i 0.00583 0.00068

53

APPENDIX III

PHYSICAL PROPERTIES OF AIR

The properties of a ir required for the calculation of

Reynolds and Nusselt numbers were the following:

1. Density, ^

2. Dynamic v i s c o s i t y , ^

3. Thermal conductivity, K

The density of a ir was determined from the equation of

state. The viscosi ty and the thermal conductivity of a ir were taken

from the tables given by Giedt (23). In Figures L7 and 18, these

properties are shown as a function of temperature only at ih.'J lb/in^abs.

pressure.

0.047

0 . 0 4 2 • " 1 1 1 ' 1 1 » 60 70 80 90 100

TEMPERATURE, (p)

PIG. 17. DYNAMIC VISCOSITY OP AIR AT ATMOSPHERIC PRESSURE

0.019

0.018

0.017

0.016

0.015

0.014 60 70 80 90 100

TEMPERATURE, (?)

PIG. 18. THERMAL CONDUCTIVITY OP AIR AT ATMOSPHERIC PRESSURE \J1

APPENDIX IV

SAMPLE CALCULATIONS

The following calculations of the heat transfer coefficient.

was done for Run 10 of the concentric annulus test. From the experi­

mental data provided in Table.IV, the values of T* were computed which

are given below.

e . (sec) (Dimensionless)

0 1.0 10 0.925 20 0.860 30 0.797 ^0 O.7J+I 50 0.693 6o 0.6UU 70 0.603

The above values are plotted in Figure 15 which gave a

straight l ine . The slope of this l ine was found to be 26 .2 hr 1 .

It was

Slope

was given by,

shown in Chapter II that,

= — . Therefore, the heat transfer coefficient C '

"-W ££0 - *-Tl BtuAr f t 2 P.

APPENDIX V

TABLES OF EXPERIMENTAL RESULTS

58

TABLE IV. TEMPERATURE-TIME DATA FOR CAPACITOR NO. 1, e.= 0. (VALUES OF T AND T a ARE IN CHART DIV.)

Run Time, 9 (sec)

0 10 20 30 40 50 60 70

.1 90.1 87.7 85.I 83.0 81.1 79-3 77-7 76.0 4i.0 2 88.8 86.0 83.5 81.1 79-0 77-0 75.2 73-4 40.0 3 86.5 83.2 80.5 77-8 75.5 73.2 71.3 69.6 39-1

4 84.0 80.6 77-6 74.7 72.2 70.0 67.8 65.9 38.5

5 83.6 80.0 76.8 74.0 71.2 68.8 66.7 64.8 38.2

6 82.7 79-1 76.0 73-1 70.4 68.0 65.9 64.0 38.0 7 83.8 80.1 76.8 73-8 71.0 68.6 66.3 64.2 37-6

.8 84.0. 79.8 76.O 72.8 70.0 67.2 64.9 62.7 37.4 9 84.8 . 80.3 76.5 73.0 70.0 67.3 65.0 62.7 37-4 10 84.0 79.4 75.3 71.7 68.6 65.7 63.3 6 l . l 37-2

11 85.8 81.0 76.6 72.8 69.5 66.5 63.8 61.6 37-0 12 82.8 78.2 74.1 70.6 67.5 64.6 62.1 60.0 36.7

13 85.4 80.2 7-5.6 71.6 68.0 65.O 62.2 59-8 36.0

59

TABLE V. DATA FOR COMPUTING REYNOLDS AND NUSSELT NUMBERS FOR CAPACITOR NO. 1, e = 0 .

Run T a e %e A h Nu

(F) ( in water) ( i b / f t 3 ) ( l /hr) (Btu/hrft 2 F)

1 79-0 0 . 0 8 .0747 16,700 17.6 7.91 88 .0

•2 78 .0 0.128 1.0746 21,100 19.8 8 .90 99-0

3 76.5 0.195 .071+6 26,100 23 .5 10.55 117.3

4 76 .0 O.285 .07U3 31,500 26.2 11-77 131.0

5 75-7 0.335 .071+5 34,200 28 .0 12.58 l 4 0 . 0

6 75:-5 0 . 3 9 0 ..0746 36,900 28 .2 12:..68 11+1.5

7 74.8 0.1+50 . 0 ^ 5 39,600 28.6 12.85 1^3.5

8 74.6 0.520 .Ojhh 1+2,700 31.7 14.23 159.2

9 7^.6 O.565 .07I+I+ 44,500 32.6 11+.65 164.0

1 0 74.5 0.630 1+6,900 35.3 15.85 177-2

l l 74 .0 0.705 .071+1+ 1+9,700 35-8 16.09 180.0

12 73-4 0 . ' 7 l a .071+8 51,250 •35-9 16.10 180.4

13 73 .0 • 0 . 818 .0747 53,750 38.1 17.10 191.8

TABLE VI. TEMPEMTURE-TIME DATA. FOR CAPACITOR WO. 1, e = 0.25 (VALUES OF T AND T a ARE IN CHART DIV.)

Run Time, G (sec)

0 10 •20 30 40 50 60 70

14 . 82.5 80.3 78.3 76.6 74.8 73-2 71.7 70.3 34.0

15 81.8 . 8 0 . 0 78.5 76.9 75-5 74.3 73.0 71.8 47.0

16 83.1 8 0 . 7 78.6 76.7 74.8 73.0 71.6 7 0 . 0 •38.0

17 81.6 79-5 77-5 75.5 73.8 72.2 70.7 69.3 4o.o 18 82.8 80.4 78.2 76 .1 74.3 72.7 71.0 6 9 . 8 4i.o

19 8 0 . 0 78 .2 76.2 74.7 73-1 71.7 70.3 6 9 . 2 48.5 20 8 1 . 8 79-7 77.6 75-7 74.0 72.3 71.0 6 9 . 7 4 7 . 0

21 79.3 77-0 75-0 73.2 71.6 7 0 . 0 68.6 67.2 46.5 22 8 1 . 9 79.3 77-0 75-0 73.0 71.3 6 9 . 8 6 8 . 3 48.0

23 7 8 . 0 75-4 73.2 71.1 69.3 67.7 6 6 . 1 64.8 46.5 2h 80.1 77.4 75.0 72.9 70.9 69.O 67.5 66.0 48.0

25 : 80.3 77.7 75.2 73-0 71.0 6 9 . 2 67 .7 66.25 48.0

26 79.2 76.6 74". l 72.0 7 0 . 0 68.2 66.7 6 5 . 2 48.5

27 82.0 79.0 76.1 73-7 71-5 69.6 67.8 66.2 48.2

28 81.2 7 8 . 0 75-2 72.8 70.6 68.6 66.8 6 5 . 1 48.0 29.. • 80.6 77.1 74.1 71.5 6 9 . 2 6 7 . 1 65.3 63.7 47.3

TABLE VII. DATA FOR COMPUTING REYNOLDS AND NUSSELT NUMBERS FOR CAPACITOR NO. 1, e = 0.25

Run T a h w

h s e %e A h Nu

• (F) (in.water) (in.water) (ib/fto (l/hr) (Btu/hrft 2 F)

l 4 73 .5 1.35 1.1 .0747 16,430 15.00 6.73 75.4 15 85-5 ."'.1.70 1.5 .0729 17,920 17.60 7.92 86 .6 16 75-5 2 .10 1.8 .0743 20,400 17.90 8.06 90.0 17 78 .0 2 .60 2 .3 .0740 22,600 18.20 8.18 ' 9 1 . 0 18 79-0 3-20 2 .8 .0742 25,050 19.82 8.92 99 .0 19 87 .O 3.90 3.4 .0730 27,080 21.90 9.85 107.5 20 8 6 . 0 4 .90 4 .3 .0735 30,550 22.32 10.05 114.6 21 85 .5 6.85 6 .2 .0738 36,200 23.94 10.77 118.0 22 87 .O 7.90 ' .7 .0 .0737 38,800 26.50 11.92 130.2 23 85 .O 9.70 8 ,7 .0742 43,300 28.20 12.69 139.0 2k 86 .5 11.30 10 .1 .0746 46,750 30.10 13.54 148.2 25 86 .5 12.40 11 .1 .0747 49,060 29.80 13.40 146.7 26 87 .O 13.40 12 .0 .0747 50,800 31.60 14.21 155.2 27 86 .5 14.45 12.9 .07-50 53,ooo 32.40 14.59 159.8 28. 86 .0 15.65 14.1 .0751 55,200 34.30 15.42 168.6 29 85.6 16.80 15 .0 .0756 57,4oo 36.80 16.55 181.0

62

TABLE VIII. TEMPERATURE-TIME DATA FOR CAPACITOR NO. 1, e = O.50 (VALUES OF T AND T a ARE IN CHART DIV.)

Run Time, Q (sec)

T a 0 10 20 30 40 . 50 60 70

3.0 86.0 84.3 82.9 81.5 80.0 78.8 77.7 76.6 47.0 31 85.0 83.1 81.5 80.0 78.5 77.1 75-9 74.8 46.0 32 86.5 84.7 82.9 81.3 80.0 78.7 77.5 76.3 48.5 33 82.2 80.5 79-0 77-6 76.I 74.8 73.7 72.6 48.6 34 82.1 80.3 78.7 77.1' 75.7 74.4 73.1 72.0 49.0

35 85.0 83.O 81.2 79-5 77.8 76.5 75-2 74.0 48.0 36 80.8 79-0 77.1 75-5 74.0 72.6 71.4 70.2 48.0 37 86.1 83.6 81.4 79.5 77.5 76.O 74.4 73.0 48.5 38 80.8 78.7 76.7 74.9 73.2 71.7 70.3 68.9 47.0

39 79-8 77-3 75-2 73.3 71.6 70.0 68.6 67.3 45.0 1+0 83.2 80.5 78.1 76.O 74.0 72.2 70.5 69.0 48.0 4i 84.4 ' 81.7 79-2 77-0 75.0 73.3 71-7 70.2 48.5 42 79-0 76.4 74.0 72.0 70.1 68.6 67.0 65.7 47.0

43 81.2 78.2 75.2 73-0 70.8 68.8 67.2 65.7 46.0 hh 81.0 77.8 74.8 72.3 70.0 67.9 66.1 64.5 45.0

TABLE IX. DATA FOR COMPUTING REYNOLDS AND NUSSELT NUMBERS FOR JCXPACITOR NO. 1, e = 0 . 5 0 .

Run e WRe A h %u

(F) (in.water) (in.water) ( l b / f t 3 ) ( l /hr) (Btu/hrft 2 F)

30 86 .2 1-5 1.25 .0728 16,580 14.17 6.37 69 .5 31 8 6 . 0 2 .1 1.90 .0730 19,620 15.81 7.12 76 .7 32 87 .0 2 .5 2 .20 .0730 21,700 16.20 7.30 79-6 33 88 .0 3.2 .2 .80 .0728 24,100 17.25 7.76 84 .6 34 88 .0 4 .0 3 .60 .0728 27,000 18.95 8.52 92 .9 35 8 7 . I 4.4 3 .90 .0730 28,800 19.10 8.60 93-7 36 87 .O 5-5 - 4 . 9 0 .0734 31,800 20.2 9.08 98.25 37 8 6 . 5 6 .7 6 .00 .0738 • 35,800 22.4 10.08 110.0 38 86 .0 6 .8 6 .00 .0737 35,600 22 .4 10.08 110.3 39 84 .0 8 .25 7 .20 .0743 39,700 23.7 IO.65 117.0 ko 8 6 . 0 10 .0 8 .80 .0740 43,150 26 .7 11.0 120.2 kl 86 .0 11.9 10.70 .0747 48,000 26.22 11.80 129.0 kl 85 .O 14.0 12.30 .0750 5 l , 4oo 28.9 13.00 142.3 43 84.0: 16.2 14.30 .0758 56,750 30.4 13.65 150.0 kk 8 3 . 0 18.15 16.05 .0758 59,900 32.25 14.50 159.5

TABLE X. TEMPERATURE-TIME DATA FOR CAPACITOR N 0 . . 1 , e = 1 . 0 (VALUES OF T. AND T a ARE IN CHART DIV.)

Run Time, 0 (sec)

T a 0 10 20 30 40 50 60 70.

45 85.2 84.0 82.9 81.9 80.8 79-9 79-0 78.8 48.7 46 80.4 78.9 77-5 76.1 74.8 73.7 72.6 71.6 38.0 47 82.2 80.7 79.3 78.0 76.7 75-5 74.5 73-5 42.0 48 78.5 77-1 75-9 74.7 73-7 72.6 71.7 70.8 45.5 49 79.7 78.3 77.0 75.8 74.8 73.8 72.6 71.8 47.O 50 80.8 79.4 78.0 76.8 75.5 74.5 73.4 72.5 48.0 51 82.5 80.8 79.3 77-9 76.5 75-3 74.2 73-0 48.3 52 85.9 83.8. 8I.9 80.0 78.5 76.9 75-5 74.2 47.5 53 84.5 82.1 80.0 78.2 76.5 75.0 73-6 72.2 47.0 54 . 85.O 82.7 8O.5 78.3 76.5 74.8 73.3 71.9 46.7 55 82.8 8O.5 78.3 76.4 74.7 73-0 71.6 70.2 46.5 56. 81.0 78.4 76.2 74.2 72.3 70.7 69.2 67.8 45.5 57 84.0 80.8 78.0 75-7 73.6 71.6 69.8 68.1 44.7 58 83.2 80.1 77.4 74.9 72.7 70.7 68.9 67-2 42.5

TABLE XI. DATA FOR COMPUTING REYNOLDS AND NUSSELT NUMBERS FOR CAPACITOR NO. 1, e = 1.0.

Run T a e NRe A h WNu (F) (in.water) (in.water) ( i b / f t 3 ) (1/hr) (Btu/hrft^)

45 88.0 1.3 1.1 .0725 15,600 11.49 5.17 56.25 46 76.0 1.3 1.2 .0743 16,070 12.25 5.51 61.50 47 79.0 1-9 1.1 .0738 19,300

21,450 12.80 5.75 63.80

48 84.0 2.4 2.2 .0734 19,300 21,450 14.13 6.35 69.70

49 85.0 3*2 2.8 .0733 24,600 15.35 6.90 75.60 50 87.0 -3-7 3-2 .0730 26,350 15.45 6.95 76.OO 51 87.0 4.7 4.1 .0730 29,700 16.90 7.60 83.00 52 86.0 6.2 5.3 .0736 34,400 19.26 8.66 94.50 53 86.5 8.4 7.2 .0740 40,200 20.00 9.00 :98'.4o 54 85.0 10.2 8.8 '.0742 44,300

47,800 22.10 9.94 108.90

55 85.0 11.8 10.2 .0747 44,300 47,800 22.15 9.95 109.00

56 83.5 13.6 11.7 .0750 51,600 24.60 11.05 121.50 57 82.0 16.05 13.8 .0755 56,200 26.22 11.80 130.00 58 80.0 18.35 15.9 .0764 65,000 26.30 11.80 130.50

66

TABLE XII. TEMPERATURE-TIME DATA FOR CAPACITOR NO. 2, e = 0 (VALUES OF T AND T a ARE IN CHART DIV.)

Run Time, 9 (sec)

T a 0 10 20 30 ko 50 60 70

59 86.6 85.O 83.5 82.0 80.7 79-3 78.2 77-0 1+7.0 60 79-7 78.0 76.5 75-2 7U.0 72.8 71.7 70.6 ^7.5 6 i 80.0 77-9 76.1 74.5 73.0 71.6 70.2 69.0 1+6.7 62 79-8 77.5 75-4 73-6 71.8 70.2 68.9 67.5 U6.0

8l.O 78.0 75.5 73-3 71.2 69.5 67.7 66.3 1+5.0 6k 79-7 76.7 73-8 71-5 69.3 6l.k 65.7 6k.2 kk. 0

65 80.2 76.5 73-3 70.4 67.9 65.7 63.7 62.0 1+3.0

TABLE XIII. DATA FOR COMPUTING REYNOLDS AND NUSSELT NUMBERS FOR CAPACITOR NO..2, e = 0

Run T a K h s e % e A . h % u

(F) (in.water) (in.water) ( l b / f t 3 ) (T/ihr) (Btu/hrft 2F)

59 86.0 1.25 1.1 .073 15 , 4 0 0 14.35 7.57 83.0 6o 86.0 2.90 2-5 .0732 23,420 17.10 9.03 99.0 61 85.O U.70 4.0 .0735 29,900 21.10 11.15 122.0 62 8U.5 7.05 6.1 .0740 36,900 23.35 12.32 135.0 63 83.O 10.il 9.0 .07U7 ^5,000 27.30 ih.ko 158.4 6h 82.0 13.2 11.k .0752 51,000 30.30 16.00 176.2 65 80.5 18.35 16.0 .0745 59,900 34.60 18.28 202.0